It's tempting to think that men who make fatuous comments about lesbians are as insignificant as the soon-to-be defunct laws that have perpetuated marriage inequality.

Men like Russell Brand, who recently told a journalist that all lesbians want to "jump the fence" – presumably with him – that those who resist his advances are "just being difficult" and something about his own noble quest to disrupt every lesbian relationship in the land.

Sadly men like Brand are all too common. Men who are so invested in a cultural narrative that requires a heterosexual female support act – real and imagined – that they label women who transgress this social rule as legitimate targets for abusive behaviour.

In the past few weeks alone I've had men ask me and my girlfriend if they can "join in" as we kiss each other goodbye, men who spot us on the tube who plonk themselves down in the seat opposite, splay their legs and rub their genitals, presumably to reassure themselves – and us? – that they are hot-blooded men despite our evident lack of interest, men who spat at us in the street, and a young man on the DLR who loudly entreated our carriage to join him in stopping us "being lesbians". On all these occasions I just had my arm around my girlfriend's shoulder.

It would be easy to dismiss some of these chaps as nutters, but this experience is so commonplace for lesbians (and bisexual women in relationships with women) that I and my team at DIVA magazine have decided to do something about it. You have to name a problem before you can address it, after all.

Inspired by the Everyday Sexism project, which documents women's daily experience of sexist piggery, we decided to launch our Everyday Lesbophobia campaign with an Everyday Lesbophobia blog, and Twitter and Facebook profiles. The response we've had so far is just the tip of the iceberg and reveals the prejudice we face.

For many of us, lesbophobia is a daily fact of life. Lesbophobia is homophobia with a side-order of sexism. It's homophobia directed particularly at lesbians. Underpinning it is the belief that women should look and behave in specific ways – keep rules that lesbians break simply by being. It encompasses the casual and subtly prejudiced celebrity media-placing that drives publicists for certain lesbian celebrities – household names you certainly will have heard of – to say no to cover interviews with DIVA. It happens in schools, workplaces, pubs and shops, on the street and in our own homes.

It comes in the form of comments that imply all lesbians are ugly and badly dressed, the "quips" from co-workers who use the word "lesbian" as if it were an insult, and the evil eye you get from men and women when you kiss your girlfriend in public. Yes, women too can be so invested in men and women dressing and behaving in line with heteronormative social codes that they cannot conceive of others living outside of this paradigm.

I've lost count of the number of times I've heard readers tell me about the treatment they receive from people who can't accept they are lesbian. One who posted on Everyday Lesbophobia told of a female colleague who told her: "You know, sometimes I can't tell if you're a man or a woman, it would be nice if you wore a dress or a skirt sometimes." Another tells of the experiences at family gatherings where the relationships, clothing and lifestyles of her heterosexual siblings are considered more important and valid than her own. There are repeated stories from gay women of all ages who have countless sorry tales of unwanted male attention that is at best belittling and at worst ends in violence.

When I'm not at DIVA, I'm a trustee for the LGBT mental health service Pace. I also volunteer as a counsellor for a young people's charity called Step Forward. Many of our gay or bisexual clients are tell us about the prejudice they face daily and we see the corrosive effect it has on their self-esteem, general wellbeing and ability to get on in life. It's no surprise to me that lesbians and bisexual women are four times more likely to suffer mental health issues than their straight female counterparts. It's this fact that underscores why we must challenge lesbophobia wherever, and whenever, it rears its scabrous head.